Method to specify the Solidify thickness based on another surface
You could add a driver to the Thickness value.



In this example, I've used the property dimension.x (it corresponds to the diameter).

If you need the value to change only at certain steps, you can set the interpolation mode to constant:


When you duplicate the sphere (alt +d), the driver will automatically update and it will mantain the reference to the proper diameter.

NOTE:
Remember to apply the scale transformation after scaling, otherwise the Thickness value will scale too.